Question

my question is factor completely by determining the GCF,pulling it to front, and putting the new expression inside parentheses 4x²+8x+2

Answer 1

The GCF is the greatest common factor. This means that we need to express all the terms by their factors and check which are common between the terms and use the one that is greatest. This is done below.

`\begin{gathered} 4x^2=2\cdot2\cdot x\cdot x \\ 8x=2\cdot2\cdot2\cdot x \\ 2=2 \end{gathered}`

Since the last term only has one factor, which is "2", the greatest common factor between them is also 2. We now need to divide each term by 2.

`\begin{gathered} (4x^2)/(2)=2x^2 \\ (8x)/(2)=4x \\ (2)/(2)=1 \end{gathered}`

We can now represent the expression by the GCF. We need to express the factor outside of the parenthesis multiplying the simplified expression given by each term divided by the factor.

`2\cdot(2x^2+4x+1)`